Y -6 INVENTORY OF SURFACE WATER RESOURCES I N SAHELIAN ZONES WITHOUT PERbtANENT HYDROLOGICAL NETWORK = by Marcel F. Roche Ingénieur en chef B Electricité de France Chef du Service hydrologique de 1 ‘ORSTOM ABSTRACT . Sahelian zones are generally too broad, have too low density of inhabitants, and toopoor surface water résources, to economically allow a dense network of hydrological stations. The method is then to keep ody a slight basic hydrological network and to study as deeply as possible the mechanism of the xunoff on selected basins considered as representative. The optimal size of these basins, in order to have the best understanding of the phenomenon, is from 2 or 5 km2 t o about 50 km2. These basins are ope- rated durirìg 3 to 5 years. A mathematical model may be fitted with the help of the collected information in order to create, by simulation, longer series, and to allow the estimation of a runoff frequency distribution curve. The studied catchmentsare classified according t o their physiographi- cal characteristics and a set of distribution curves can be drawn for each class or standard basin and for different values of the median yearly pre- cipitation. So a set of graphes can be established, which can be used to estimate the runoff distribution for unknown catchments, after a field survey of them followed by an analysis of their physiographical conditions.
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Y -6
I N V E N T O R Y OF SURFACE WATER RESOURCES I N S A H E L I A N ZONES
WITHOUT PERbtANENT H Y D R O L O G I C A L NETWORK
= b y Marcel F. Roche
Ingénieur en chef B Elec tr ic i té d e France
Chef du Service hydrologique de 1 ‘ORSTOM
A B S T R A C T
. Sahelian zones are generally too broad, have too low density o f inhabitants, and toopoor surface water résources, t o economically allow a dense network o f hydrological stations. The method i s then t o keep o d y a s l i g h t basic hydrological network and t o s t u d y a s deeply a s possible the mechanism of the xunoff on selected basins considered as representative. T h e optimal s i ze o f these basins, i n order t o have the best understanding o f the phenomenon, i s from 2 or 5 km2 t o about 50 km2. These basins are ope- r a t e d dur ir ìg 3 t o 5 years . A mathematical model may be f i t t e d w i t h the help of the collected information i n order t o create, b y simulation, longer ser ies , and t o allow the estimation o f a runoff frequency distribution curve. The studied catchmentsare c l a s s i f i e d according t o their physiographi- c a l characteristics and a se t o f distribution curves can be drawn f o r each class or s t a n d a r d basin and f o r d i f f e ren t values o f the median yearly pre- c ipi tat ion. So a se t o f graphes can be established, which can be used t o estimate the runoff distribution f o r unknown catchments, a f t e r a f i e l d survey o f them followed b y an analysis o f the ir physiographical conditions.
1. 1NTRODU.CTION . -
1.1. The word llSAHELIAN1l is t a k e n h e r e i n t h e g e n e r a l meaning f o r Africa
i n t h e S o u t h of S a h a r a . As f a r as h y d r o l o g y is c o n c e r n e d , i t is g e n e r a l l y ad-
m i t t e d t h a t t h e " S a h e l i a n zone" is i n c l u d e d i n t h e i n t e r t r o p i c a l zone and dé-
l imi ted by t h e i s o h y e t s 300 and 750 mm.
1.2. The main f e a t u r e o f t h e s a h e l i a n b a s i n s i s t h e phenomenon of "hydro-
g r a p h i c d e g r a d a t i o n " less r e m a r k a b l e t h a n i n d e s e r t i c or s u b d e s e r t i c z o n e s , b u t
still v e r y clear. It c o n s i s t s i n a p r o g r e s s i v e v a n i s h i n g of t h e stream b e d s from
ups t ream t o downstreamc The i n t e n s i t y of t h e phenomenon depends c h i e f l y on t h e
d r y n e s s of t h e climate, b u t a l s o on morphology ( e s p e c i a l l y s l o p e s ) and t y p e s o f
s o i l . But mean relief and s o i l d e g r a d a t i o n s are by some d e g r e e c o r r e l a t e d t o t h e
s ize of t h e ca tchment . I n t h e most p a r t of the s a h e l i a n zone , t h e h y d r o g r a p h i c
d e g r a d a t i o n g e n e r a l l y d o e s n o t a p p e a r below 400-500 kin2* Above 1000 km2, streams
are almost a l w a y s affected by t h i s d e g r a d a t i o n ,
1.3. The p r e c e d i n g remark l e a d s t o c l a s s i f y s a h e l i a n c a t c h m e n t s a c c o r d i n g
t o t h e i r size, For i n s t a n c e , i n t h e s t u d y c a r r i e d o u t by Dr. R o d i e r on t h e b a s i s
of r e s u l t s o b t a i n e d 'from ORSTON's r e p r e s e n t a t i v e b a s i n s i n A f r i c a n S a h e l , f i v e
classes have been c o n s i d e r e d :
a - a few h e c t a r e s s i z e d c a t c h m e n t s ;
b - 2 t o 40 km2 ;
c - 40 t o 500 km2, ex tended i n c e r t a i n cases t o 600 and e v e r 800 km2
f o r r e l a t i v e l y weak h y d r o g r a p h i c d e g r a d a t i o n ;
d - more t h a n 1000 km2 ;
e - more t h a n 10000 km2.
1.4. The class 2 t o 40 km2 is t h e most i m p o r t a n t f o r s u r f a c e water economy
i n Saheliàn a f r i c a n zone ( s i t e s f o r small r e s e r v o i r s ) . I n a d d i t i o n , i t c o r r e s -
ponds i n Africa t o t h e most c u r r e n t s ize of r e p r e s e n t a t i v e ca tchment : f o r t h a t
we c a n d i s p o s e o f t h e b e s t and more c o m p l e t e i n f o r m a t i o n . T h i s p a r t will be
t r e a t e d i n d e t a i l .
1.5. The aim of t h i s l e c t u r e is t o e x p l a i n h o w . t o make a n - a s s e s s m e n t of
water s u r f a c e r e s o u r c e s i n a S a h e l i a n zone. It t a k e s as a n example t h e s t u d y rea-
l i z e d by Dr. R o d i e r , w i t h t h e h e l p of Mr. Girard l , a n h y d r o l o g i s t s p e c i a l i s t
i n m a t h e m a t i c a l ’ m o d e l i n g f o r c a t c h m e n t b e h a v i o r . Such a k i n d of s t u d y n e c e s s i t s
local i n f o r m a t i o n b u t some of t h e r e s u l t s may be c a u t i o u s l y e x t r a p o l a t e d t o a n o t h e r similar r e g i o n s .
2. G e n e r a l p r i n c i p l e s f o r s u r f a c e water a s s e s s m e n t i n s a h e l i a n r e g i o n s .
[I
2.1. Among o t h e r s , t h e methodology will depend o n t h e s ize of t h e c a t c h -
ments a c c o r d i n g . t o t h e c l a s s i f i c a t i o n g i v e n i n 1.3. However, a common p l a n c a n
be d e s c r i b e d a t least f o r classes a ) t o d ) .
2.2. Data c o l l e c t i o n .
The first s t e p is t o assess t h e . a v a i l a b l e i n f o r m a t i o n e s p e c i a l l y i n
c l i m a t o l o g y ( o v e r a l l r a i n f a l l d a t a ) and i n hydrometry.
2.2.1. R a i n f a l l d a t a .
2.2.1.1. The p r o c e s s i n g is t h e same whatever is t h e s ize of t h e c a t c h -
ment. I n A f r i c a n S a h e l , f o r i n s ’ t a n c e , more t h a n 70 s t a t i o n s w i t h good r e c o r d s
c a n b e s e l e c t e d , some of them h a v i n g l o n g p e r i o d s of r e c o r d i n g . The p r o c e s s i n g
c o n s i s t s , f o r e a c h s t a t i o n , i n computing t h e mean and t h e median y e a r l y t o t a l
( i s o h y e t a l maps) and i n s t u d y i n g t h e f r e q u e n c y d i s t r i b u t i o n of y e a r l y t o t a l s .
2.2.1.2. F i g u r e 1 g i v e s t h e i s o h y e t a l maps (medians)- f o r West and
[ll) C e n t r a l Africa from S a h e l i a n t o d e s e r t i c z o n e s ( e x t r a c t e d from r e f e r e n c e
The f r e q u e n c y d i s t r i b u t i o n of y e a r l y t o t a l s depends on t h e v a l u e of t h e median
and a s t u d y c a r r i e d o u t by a method of y e a r s - s t a t i o n s showed t h a t t h e d i s t r i b u -
t i o n c a n b e e x p r e s s e d by a g e n e r a l i z e d e x p o n e n t i a l law as 1/0.4
F (excedence p r o b a b i l i t y ) = 1 - e x p [- xo ] w i t h xo = 7.6 x loe4 Pm2 - 52.4
S = 1.1579 (Pm - x0)
n Pm b e i n g t h e median v a l u e of t h e a n n u a l r a i n f a l l s . The r e p r e s e n t a t i v e c u r v e s of
1
6
>*
x
*
t h i s fo rmula are g i v e n on F i g u r e 2.
2.2.2. H y d r o l o g i c a l d a t a .
2.2 -2.1. They come f rom s e v e r a l o r i , g i n s . c o r r e s p o n d i n g t o t h e v a r i o u s
gaug ing and s u r v e y o p e r a t i o n s , from r e g u l a r h y d r o m e t r i c ne twork t o s p e c i f i c ( o r
l o c a l ) measurements c a r r i e d o u t d u r i n g s h o r t p e r i o d s . I n s a h e l i a n r e g i o n s r e g u l a r
s t a t i o n s ve ry r a r e l y o p e r a t e d for ca t chmen t areas below 500. t o 1000 km2 . O n t h e o t h e r
hand, s a h e l i a n b a s i n s w i t h areas e q u a l o r g r e a t e r t h a n 10000 km2 are a l s o v e r y
seldom. I n A f r i c a n S a h e l , for i n s t a n c e , o n l y 7 o r 8 b a s i n s of t h i s t y p e e x i s t
f rom S e n e g a l t o Sudan.
2.2.2.2. For t h e most p a r t o f t h e ca t chmen t s , b a s i c h y d r o l o g i c a l d a t a
are p r o v i d e d by r e p r e s e n t a t i v e b a s i n s y t o g e t h e r w i t h a n a n a l y s i s o f t h e r a i n -
f a l l - d i s c h a r g e r e l a t i o n s h i p l e a d i n g among o t h e r s t o estimate t h e r u n o f f c o e f -
f i c i e n t and its v a r i a t i o n s . I n t h e example of ORSTOM s t u d i e s i n A f r i c a n Sahel,
a l o t o f r e p r e s e n t a t i v e b a s i n s have been worked o u t from 1955 t o 1971. They can
p r o v i d e p r e c i s e v a l u e s on y e a r l y r a i n f a l l and r u n o f f , t h e d u r a t i o n o f o b s e r v a -
t i o n s n o t e x c e e d i n g 3 o r 4 y e a r s ; it is i n s u f f i c i e n t t o p r o v i d e a s t a t i s t i c a l
r
1 L
series, b u t it is s u f f i c i e n t i n t h e most p a r t o f t h e cases t o a l l o w t h e f i t t i n g
of a m a t h e m a t i c a l ca tchment b e h a v i o u r model ; t h e n a s t a t i s t i c a l series of a n n u a l
r u n o f f may b e d e r i v e d from a l o n g r a i n f a l l series which is o f t e n a v a i l a b l e .
2.2.2.3. Another s o u r c e s o f i n f o r m a t i o n comes f rom r e g i o n a l s t u d i e s
c a r r i e d d u r i n g 1 t o 4 y e a r s and a l so g i v i n g d a t a i n t h e f i e l d s o f r a i n f a l l and
r u n o f f . The t y p e o f i n f o r m a t i o n is close t o t h i s o n e o f r e p r e s e n t a t i v e b a s i n s
b u t t h e size of t h e c a t c h m e n t s is g e n e r a l l y g r e a t e r i n a n a v e r a g e , and t h e ob-
s e r v a t i o n s n o t s o i n t e n s i v e and d e n s e i n t h e s p a c e .
2.2.2.4. The case of g r e a t t r o p i c a l r i v e r s c r o s s i n g t h e s a h e l i a n
zone must b e t a k e n a p a r t . T h i s r i v e r s , l i k e Nile, C h a r i , N i g e r , S e n e g a l , a re
f e d by humid t r o p i c a l zones and do n o t p r e s e n t any c h a r a c t e r i s t i c of s a h e l i a n
stream. On a n o t h e r hand, t h e i r reg imen are p r e t t y well known from c l a s s i ca l
b a s i c ne tworks .
.h
A.
r
- 4 -
k,
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P'
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li
2 . 3 . Methodology fo r water r e s c u r c e s a s s e s s m e n t
2.3.1. Class e) : area g r e a t e r t h a n 10000 km
These b a s i n s are g e n e r a l l y u s e l e s s f o r s u r f a c e water management ; t h e
2
median a n n u a l s u r f a c e f l o w is n u l l f o r t h e most of them. I n a d d i t i o n , t h e y u a n t i -
t a t i v e i n f o r m a t i o n a b o u t t h e i r f l o w is v e r y scarse and t h e knowledge o f r a i n f a l l ,
i f any , is n o t v e r y h e l p f u l . However, t h e knowledge of t h e s u r f a c e r u n o f f may
o n l y come from t h e d i r e c t o b s e r v a t i o n of t h e d i s c h a r g e s ( c l a s s i c a l ne twork) and
t h e most p a r t of t h e time one c a n o n l y g i v e some o r d e r s of magnitude. An example
is g i v e n on f i g u r e 3 : r u n o f f d e p t h s a g a i n s t p r o b a b i l i t i e s of exceedence . The
g e o g r a p h i c a l t r a n s p o s i t i o n is i m p o s s i b l e .
2.3.2. Class d ) : area between 1 O00 and 10 O00 kmL
2.3.2.1. The h e t e r o g e n e i t y of t h e s e c a t c h m e n t s is st i l l too h i g h f o r
e s t a b l i s h i n g a r e l i a b l e lumped r a i n f a l l - r u n o f f r e l a t i o n s h i p . It is p o s s i b l e , and
i t h a s been made by G, ) f o r t h e c a t c h m e n t o f Oued Ghorfa
( M a u r i t a n i a ) , t o .fit a complex model t o t h e r e s u l t s o b t a i n e d by a r e g i o n a l s t u d y ,
a n d e v e n t u a l l y t o produce a l o n g a n n u a l r u n o f f series by s i m u l a t i o n , b u t t h i s
r e m a i n s f o r t h e s t u d i e d ca tchment i tself and c a n n o t be t r a n s p o s e d t o a n o t h e r one .
2.3.2.2. However, some g r e a t l i n e s may b e e s t a b l i s h e d f o r a r a t h e r qua-
[Il ' l i t a t i v e e s t i m a t i o n o f a n n u a l r u n o f f i n t h i s c lass of b a s i n s . I n h i s s t u d y
Dr. R o d i e r d i s t i n g u i s h e s 2 s e p a r a t e g r o u p s :
2.3.2.2.1. B a s i n s on g r a n i t e o r g r a n i t o - g n e i s s - They have been s t u d i e d , i n A f r i c a n S a h e l , c h i e f l y i n Ouaddaï (Chad) ,
i n t h e n o r t h o f Upper-Volta (Djibo, Lake of Bam), t h e V o l t a ï a n t r i b u t a r i e s of
Niger R i v e r ( D a r g o l , Gorouol) , t h e E a s t e r n Upper-Volta ( G o u l b i of Haradi)
r u n o f f c o e f f i c i e n t f o r median y e a r v a r i e s from 1 t o . 5 % and t h e f r e q u e n c y i s shown
on f i g u r e 4. Of c o u r s e , i t is p o s s i b l e t o d e s c r i b e t h e g e n e r a l c h a r a c t e r i s t i c s
of t h e p l o t t e d c a t c h m e n t s , b u t t h e s e c h a r a c t e r i s t i c s are too complex t o p r o v i d e
The
a n u s e f u l t o o l f o r a r e a l e x t r a p o l a t i o n o f t h e r e s u l t s t o a n o t h e r c a t c h m e n t s .
However, a s i m p l e comparison between t h e c h a r a c t e r i s t i c s ( i n c l u d i n g mean a n n u a l -
- 5 - I
r a i n f a l l ) of any ca tchment t o b e deve lopped and t h o s e o f one o f t h e c a t c h m e n t s
p l o t t e d on f i g u r e 4,may p r o v i d e a n o r d e r of magni tude o f t h e s u r f a c e water deve-
lopment p o s s i b i l i t i e s .
2.3.2.2.2. Clayey b a s i n s on s c h i s t , m a r l y - l i m e s t o n e , etc.
The e f f i c i e n c y o f t h e s e b a s i n s i s b e t t e r t h a n t h i s o n e o f t h e p r e -
c e d i n g group. The r u n o f f c o e f f i c i e n t f o r median y e a r v a r i e s f rom 3 t o 14 %. I n
t h e ORSTOM s t u d i e s , t h e conce rned r e g i o n s are e s p e c i a l l y t h e Gorgo1 Noir, t h e
Brakna and t h e Ghorfa i n M a u r i t a n i a , t h e Ader Dou tch i and t h e Waggia i n Nige r .
Same remarks as f o r item 2.3.2.2.1. T h e f r e q u e n c y d i s t r i b u t i o n of a n n u a l - r u n o f f
d e p t h s is p l o t t e d on f i g u r e 5.
2.3.5. Class c) : area between 40 and 1 O00 kmL
2.3.3.1. The i n f o r m a t i o n comes c h i e f l y from r e p r e s e n t a t i v e b a s i n s and
f rom r e g i o n a l s t u d i e s . However, c e r t a i n r e s u l t s coming from r e g u l a r ne tworks may
still b e used . For Afr i can S a h e l a b o u t 42 r e p r e s e n t a t i v e c a t c h m e n t s are a v a i l a b l e .
The r e l a t i o n s h i p s between r a i n f a l l and r u n o f f are s t i l l d i f f i c u l t t o b e e s t a b -
l i s h e d . However, t h e runof f c o e f f i c i e n t computed for t h e median y e a r l y p r e c i p i -
t a t i o n s a l l o w s t o a p p r e c i a t e t h e r e l a t i v e i m p o r t a n c e o f r u n o f f from one b a s i n t o
a n o t h e r . .
2.3.3.2. The median v a l u e o f t h e r u n o f f c o e f f i c i e n t c h i e f l y depends ,
i n a d d i t i o n t o t h e mean a n n u a l r a i n f a l l , on t h e s o i l s characterist ics g e n e r a l l y
d e r i v e d f rom t h e g e o l o g i c a l s t r u c t u r e of t h e ca t chmen t . I n A f r i c a n S a h e l , f o r
i n s t a n c e , Dr. R o d i e r h a s c o n s i d e r e d two g e o l o g i c a l classes of c a t c h m e n t s f o r
area class c.
2.3.3.2.1. Bas ins on g r a n i t e and g r a n i t o - g n e i s s - I n these b a s i n s , t h e h y d r o g r a p h i c a l d e g r a d a t i o n is v e r y f r e q u e n t ,
o v e r a l l i n t h e n o r t h and i f t h e s l o p e s i n t h e b a s i n are n o t t o o h igh . As a r u l e ,
t h e p e r m e a b i l i t y is g r e a t and t h e r u n o f f c o e f f i c i e n t s are low t o v e r y low. T h e i r
median v a l u e s v a r y from less t h a n 1 % t o 6-7 %.
2.3.3.2.2. Basins on o t h e r s o i l s (marls, sandy s o i l s , l a t e r i t i c
c u i r a s s e s , s a n d s t o n e , s c h i s t s and c l a y s ) . The d e g r a d a t i o n is less marked t h a n
fo r b a s i n s on g r a n i t e , and c a n be shown o n l y f o r
g e n e r a l l y less p e r v i o u s and t h e s l o p e s are s h a r p e r . Except f o r s p e c i a l c o n d i -
t i o n s , v e r y seldom i n t h a t case, a s a g r e a t i m p o r t a n c e of wind s a n d d e p o s i t , t h e
median r u n o f f c o e f f i c i e n t g o e s from 5 t o 19 %.
g r e a t e r areas. The s o i l s are
O f c o u r s e , t h e v a r i a t i o n s of t h e r u n o f f c o e f f i c i e n t i n s i d e o f e a c h g e o l o -
g i c a l class are due e s p e c i a l l y t o
- t h e v a r i a t i o n o f t h e size of t h e c a t c h m e n t (40 t o 1 O00 km2), t h e ' coeffi-
c i e n t d i m i n i s h i n g when t h e size i n c r e a s e s ,
- t h e v a r i a t i o n o f t h e median a n n u a l r a i n f a l l (300 t o 750 mm).
2.3.3.3. Frequency d i s t r i b u t i o n of a n n u a l r u n o f f
The most e f f i c i e n t t o o l i n o r d e r t o e v a l u a t e t h e s u r f a c e water r e s c u r -
ces i n s a h e l i a n zone is t h e g r a p h of t h e a n n u a l runoff a g a i n s t i ts f r e q u e n c y ,
d e r i v e d f o r e a c h t y p e of c a t c h m e n t , from t h e p r e c e d i n g i n f o r m a t i o n and s t u d i e s . Y
F o r S a h e l i a n Africa, t h e f r e q u e n c y c u r v e s e s t a b l i s h e d f o r b a s i n s on 7 ri g r a n i t e o r g r a n i t o - g n e i s s , are g i v e n on f i g u r e 6 . The same c u r v e s b u t f o r t h e
s e c o n d g e o l o g i c a l class are g i v e n on f i g u r e 7.
Each c u r v e c o r r e s p o n d s t o t h e e s t i m a t i o n s macle f o r a g i v e n s t u d i e d
b a s i n , d e s c r i p t i o n of which is g i v e n i n t h e t e x t of r e f e r e n c e 1 (3.A. R o d i e r ) .
F o r a n unknown c a t c h m e n t , it is n e c e s s a r y t o examine c a r e f u l l y t h e v a r i o u s cha- [I
racteristics of it and t o c h o o s e t h e closest b a s i n t y p e b e f o r e e n t e r i n g i n t o
t h e g r a p h s 6 o r 7.
2 2.3.4. Class b : area between 2 and 40 km
It will e x p l a i n e d i n d e t a i l l a t e r on i n a s p e c i a l c h a p t e r .
2.3.5. Class a : area : a f e w . h e c t a r e s
2.3.5.1. T h i s is t h e f i e l d of impluviums fo r c i s t e r n s w h i c h c a n a l so
be i n t e r e s t i n g f o r v e r y small r e s e r v o i r s . I n A f r i c a n S a h e l , some i n f o r m a t i o n i s
a v a i l a b l e f o r r a i n f a l l - r u n o f f r e l a t i o n s h i p i n v a r i o u s c o n d i t i o n s . The r u n o f f -
c o e f f i c i e n t s are as follow ( i s o h y e t of a b o u t 600 m m ) :
I - 7 -
I
I n median y e a r
- Clayey s o i l s w i t h medium s l o p e 40 t o 50 % ( t y p e A )
- Soi l s c o v e r e d by a t h i c k l a y e r of l a te r i t i c
g r a v e l s w i t h non n e g l e c t a b l e v e g e t a b l e c o v e r 4 t o 8 % ( t y p e C)
( t y p e A )
( t y p e C)
- C l a y s d e r i v e d from s c h i s t s
- G r a n i t e s wea the r i n b l o c k s
40 t o 50 %
less t h a n t o 10 S
- G r a n i t i c g l a c i s w i t h modera t e s l o p e s 30 % ( t y p e 8)
I n v e r y r a i n y y e a r s ( a b o u t 100 y e a r s - f r e q u e n c y )
- Type A : 60-70 %
- Type B : 40-50 %
- Type C : 20-30 %
I n v e r y d r y y e a r ( a b o u t 100 y e a r s - f r e q u e n c y )
- Type A : 25-30 X
- Type 6 : 5-10 %
- Type C : O- 5 %
2.3.5.2. P r a c t i c a l d e t e r m i n a t i o n of t h e r u n o f f
- Deduce f rom f i g . 1 t h e y e a r l y p r e c i p i t a t i o n f o r t h e ca t chmen t i n evo lu -
t i o n (median v a l u e ) .
- I n t r o d u c i n g t h i s median v a l u e i n t o f i g . 2 , choose t h e n e a r e s t y e a r l y
r a i n f a l l f r e q u e n c y d i s t r i b u t i o n c u r v e (by i n t e r p o l a t i n g i f n e c e s s a r y ) .
- F i e l d e x a m i n a t i o n o r , i f i m p o s s i b l e , e x a m i n a t i o n of aer ia l p h o t o g r a p h s ,
i n o r d e r t o r e d u c e t h e a c t u a l unknown b a s i n t o a s t u d i e d case.
- Determine t h e f r e q u e n c y d i s t r i b u t i o n c u r v e of y e a r l y r u n o f f , f rom t h r e e
p o i n t s ( c o r r e s p o n d i n g t o v e r y d r y , medium and v e r y r a i n y y e a r s , computed
f rom t h e r a i n f a l l s w i t h t h e h e l p o f c o e f f i c i e n t s g i v e n above.
3. D e t a i l e d s t a t e m e n t on t h e methodology f o r b a s i n s w i t h areas between 2 an 40 km2
3.1. T h i s area i n t e r v a l i s v e r y i n t e r e s t i n g because it c o r r e s p o n d s t o t h e
e most f r e q u e n t need f o r water development i n s a h e l i a n r e g i o n s and c o n s e q u e n t l y i
h a s been p r e t t y well s t u d i e d . I n a d d i t i o n , c a t c h m e n t s o f s u c h s izes may be c o n s i -
d e r e d as p h y s i c a l c l n i t s a s well from t h e p o i n t o f view o f phys iog raphy a s from
I - 8 - ~~ ~
f
t h i s one o f meteoro logy . T h i s is t h e r e a s o n why t h i s p o i n t merits a s p e c i a l
s t a t e m e n t i n o u r pape r .
3.2. The i n f o r m a t i o n g e n e r a l l y comes from r e p r e s e n t a t i v e ca t chmen t s . For
t h e s t u d y of Dr. R o d i e r i n A f r i c a n S a h e 1 , t h e r e s u l t s of 41 r e p r e s e n t a t i v e b a s i n s
have been used. These b a s i n s have been c l a s s i f i e d a c c o r d i n g t o t h e i r g e o l o g i c a l
c o m p o s i t i o n and its i n c i d e n c e on t h e p e r m e a b i l i t y , i n o r d e r t o f a c i l i t a t e t h e
a n a l y s i s of t h e v a r i o u s f a c t o r s . T a b l e I shows t h i s c l a s s i f i c a t i o n , It c o v e r s
o n l y t h e cases for which f i e l d s t u d i e s have been c a r r i e d o u t .
As a matter o f fac t , e v e r y c a t c h m e n t is p h y s i c a l l y complex and b a s i -
c a l l y non homogeneous. So i t would be u n r e a l l i s t i c t o c l a s s i f y a l l t h e p o s s i b i -
l i t i es i n c l u d i n g c o m b i n a t i o n s o f a l l p o s s i b l e components and t o t r y t o e x p l i c i t
t h e s p e c i f i c i n f l u e n c e o f them on t h e r a i n f a l l - r u n o f f r e l a t i o n s h i p . It a p p e a r e d
i t would be b e t t e r t o choose some c h a r a c t e r i s t i c c a t c h m e n t s b e h a v i o u r o f which
b e r e p r e s e n t a t i v e o f a set o f s t u d i e d
i s c a l l e d " s t a n d a r d b a s i n " f o r g i v e n c o n d i t i o n s . The list o f " s t a n d a r d b a s i n s "
is g i v e n i n T a b l e II.
or u n s t u d i e d ca t chmen t s . Such a ca t chmen t Y
I 6,
3.3. Frequency d i s t r i b u t i o n o f r u n o f f ( s t a n d a r d area : 25 I") 3.3.1. A r e p r e s e n t a t i v e b a s i n i s o p e r a t e d , on a a v e r a g e , d u r i n g 3 y e a r s .
It is v e r y a r b i t r a r y , under t h o s e c o n d i t i o n s , t o d e t e r m i n e t h e mean v a l u e o r t h e
median of t h e r u n o f f d e p t h o r of t h e r u n o f f c o e f f i c i e n t . On t h e o t h e r hand, t h i s
i n f o r m a t i o n is s u f f i c i e n t t o f i t a m a t h e m a t i c a l model s i m u l a t i n g t h e r u n o f f
b e h a v i o u r o f t h e ca tchment . I n t h e s t u d y of Dr. R o d i e r , t h e " s i m p l i f i e d model" of
G. G i r a r d h a s been used .
3.3.1.1. T h i s model (see r e f e r e n c e 3 ) is o p e r a t i n g w i t h d a i l y p r e - [I c i p i t a t i o n s , b u t t h e r e s u l t s are v a l i d o n l y mon th ly or b e t t e r y e a r l y .
The p r i n c i p l e s are f o l l o w i n g :
t h e " e f f i c i e n t p r e c i p i t a t i o n " HU ( a b l e t o g i v e r u n o f f ) is related t o t h e
"-
i
t o t a l d e p t h HT o f t h e s t o r m by t h e mean r e l a t i o n s h i p :
HU = a ( H t - '5)
- 9 -
TABLE I
B A S I N S WITH A R E A BETWEEN 2 A N D 4 0 K M 2
Classif ication according t o geological consti tution
1. Sandy s o i l s . - Dunes (dead o r a c t i v e )
2. G r a n i t e and - G r a n i t i c a r e n a s (more o r - Wind d e p o s i t c o v e r
g r a n i t o - g n e i s s less deep)
3. Sands tone "I
- Glacis o r ped imen t s s a n d y - c l a y s o i l s r e g s - o u t c r o p s - Smal l streams beds ( u p p e r p a r t o f ca t chmen t s )
_. Coarse sand on t h e bot tom, sandy c l a y banks - Downstream, v a l l e y s bot tom w i t h hydromorphic soils - Later i t ic g r a v e l s f rom d e s t r u c t i o n of c u i r a s s e s
- S u b h o r i z o n t a l l a y e r s
- Sandy s o i l s on s a n d s t o n e g e n e r a l l y s h a l l o w - Sandy-c lay a l l u v i u m i n v a l l e y bot tom - Laterit ic c u i r a s s e s c o v e r i n g s a n d s t o n e - washed f e r r u g i n o u s t r o p i c a l s o i l s unde r c u i r a s s e s
- Black c l a y s on marls or mar ly l i m e s t o n e s o r s andy c l a y e y c o l l u - vium and f e r r u g i n o u s s o i l s
4. Marly s a n d s
5. S c h i s t s - Clay and sandy c l a y f rom w e a t h e r i n g o f s c h i s t s
6. C o n t i n e n t a l - H o r i z o n t a l t a b l e s o r r i d g e s t e r m i n a l from f e r r u g i n o u s s a n d s t o n e
more o r less wea the red
- 10 -
very p e r v i o u s
p e r v i o u s b u t r a p i d l y s a t u r a t e d when s h a l l o w
i m p e r v i o u s
v e r y p e r v i o u s
i m p e r v i o u s when w e t t e d
p e r v i o u s if t h e l a y e r i s t h i c k e r t h a n 15-20 cm - impervi0u.s when compact - p e r v i o u s screes o r
i m p e r v i o u s when s a t u r a t e d d i a c l a s e s
r a t h e r i m p e r v i o u s
g e n e r a l l y i m p e r v i o u s
r a t h e r i m p e r v i o u s
r a t h e r i m p e r v i o u s
p e r v i o u s
TABLE I ( su i t e )
C l a s s i f i c a t i o n . C o m p o n e n t s P e r m e a b i li t y --------------------------- ...................................... ...................... i
6 . C o n t i n e n t a l t e r m i n a l ( su i t e l - On t h e s l o p e s : marly lime
s t o n e s and more o r less c l a y e y c o l l u v i u m
- Brown-red s o i l s on material from s a n d s t o n e - c u l t i v a t e d areas - Sands i n t h e bed of t h e streams ( u p p e r p a r t of t h e c a t c h m e n t s )
- Downstream : hydromorphic s o i l s .
i m p e r v i o u s
r a t h e r p e r v i o u s
p e r v i o u s
i m p e r v i o u s
- 11 -
I-
>
T A B L E I I
EASIN .AREA.5 . BETWEEN 2 AND 4 0 K M 2
S t a n d a r d basins
Desi g n a t i on Areas Median annual Median r u n o f f r a i n f a l l . C o e f f i c i e n t C l a s s i f i cation
% ( s e e T a b l e I )
No V I 1 of Niamey Abou Goulem
Barlo Barlo II Cagara-Ouest Koubaka II Sebikotane II Sebikotane III Kadiel Pô
Kountkouzout
20 12.3 17.8 36.6 28
30 43
2.6 39.5 2.7 16.6
600 410
790-800 790-800 400-420
570 620
620 450-475 . 450 390-400
0.5 4.2
10-12 6-10 12
17 6-7
10-12 10
30 15
1 2 2
2 : 2
3
4
4 5 5 6
- 12 -
The r u n o f d e p t h LR g e n e r a t e d by a storm is related t o HU by
LR = K (HU - SU)
. Mixing b o t h e q u a t i o n s ? .one c a n write
LR = KO ( H t - HO)
. Ho c h i e f l y depends o n . s o i l m o i s t u r e i n t h e c a t c h m e n t and v a r i e s f rom
O t o Ho max. I n t h e model, it; is computed from a n i n d e x
= (H3 + H t j ) C "3 + 1 H j b e i n g a p r e c i p i t a t i o ' n i n d e x fo r t h e day 3 .and
H t j t h e t o t a l p r e c i p i t a t i o n on t h e same day
C is a f i t t i n g coefficient o f t e n n e a r 0.7
If H j > Ho max. Ho = O
I f O C H ~ C H ~ max HO = HO max - ~j I n t h e p r a c t i c e , KO and Ho max are f i t t i n g p a r a m e t e r s .
3.3.1.2. Such model was f i t t e d on t h e r e s u l t s of two r e p r e s e n t a t i v e
c a t c h m e n t s i n A f r i c a n S a h e l , q u i t e d i f f e r e n t by t h e i r r u n o f f b e h a v i o u r .
The c a t c h m e n t of K a d i e l , l i t t l e p e r v i o u s , has a n area o f 39 km2 and
a mean p r e c i p i t a t i o n of 475 mm. One found f o r t h e model Ho max = 27, KO = 0.60.
42 y e a r s c o u l d be s i m u l a t e d from r a i n f a l l d a t a of t h e t h r e e s t a t i o n s . The ana-
l y s i s of t h i s sample a l l o w e d t o draw t h e f r e q u e n c y d i s t r i b u t i o n c u r v e f o r a
K a d i e l s t a n d a r d b a s i n , c o r r e s p o n d i n g t o a mean y e a r l y r a i n f a l l of 450 .rom. T h i s
c u r v e is a l s o c o n s i d e r e d a s v a l u a b l e f o r 25 km 2 . The c a t c h m e n t of Abou Goulem is v e r y p e r v i o u s and h a s a n area of
12.3 km2 and a mean p r e c i p i t a t i o n of 400 mm. The v a l u e s of t h e p a r a m e t e r s of
t h e model are Ho max = 24 mm and KO = 0.22. The r e s u l t s of t h e s i m u l a t i o n g i v e ,
after r e d u c t i o n t o 25 km2, a f r e q u e n c y c u r v e d e f i n e d by t h e f o l l o w i n g v a l u e s of
r u n o f f :
985 f r e q u e n c y of exceedence : O
. 965 : 1 mm
. median : 12 mm
II
. O 1 f r e q u e n c y . o f exceedence : 104 mm
- 13 - 1
c..
c
Y
From t h e s e c u r v e s e s t a b l i s h e d f o r 400 mm (Abou-Goulem) and 450 mm
( K a d i e l ) , o n e d e r i v e d s imi la r c u r v e s for median r a i n f a l l s between 300 and 750 mm.
T h i s e x t r a p o l a t i o n is based
- o n t h e fact t h a t t h e r u n o f f c o e f f i c i e n t is i n c r e a s i n g w i t h t h e r a i n f a l l ,
- t h e c o n s i d e r a t i o n of o t h e r c a t c h m e n t s h a v i n g similar c h a r a c t e r i s t i c s and
d i f f e r e n t median a n n u a l r a i n f a l l .
The c o r r e s p o n d i n g sets of c u r v e s are drawn i n f i g u r e s 8 and 9.
3.3.2. For e a c h s t a n d a r d b a s i n c a t a l o g u e d i n T a b l e II, t h e f r e q u e n c y
d i s t r i b u t i o n c u r v e s of r u n o f f have been drawn w i t h t h e h e l p o f t h e r e s u l t s ob-
t a i n e d on r e p r e s e n t a t i v e b a s i n ( e s p e c i a l l y : r u n o f f d e p t h and r u n o f f c o e f f i c i e n t
fo r median y e a r l y p r e c i p i t a t i o n ) , and u s i n g a s a g u i d e t h e c u r v e s of g r a p h 8 o r
9 a c c o r d i n g t o t h e t y p e a d o p t e d for t h e c o n c e r n e d s t a n d a r d b a s i n . The r e s u l t s are
g i v e n on f i g u r e 10.
2 3.4. Frequency d i s t r i b u t i o n of r u n o f f ( s t a n d a r d area 5 km )
The methodology and t h e g e n e r a l p r i n c i p l e s are e x a c t l y t h e same a s
above, b u t i n numerous cases, t h e r u n o f f c o n d i t i o n s are too d i f f e r e n t fo r u s i n g
t h e same c u r v e s . F o r p e r v i o u s areas, t h e key b a s i n is still t h i s o n e of Abou-
Goulem (12.5 km2, between 5 and 251, b u t t h e i m p e r v i o u s areas are r e p r e s e n t e d
by t h e Po b a s i n (2.7 km2). The d i s t r i b u t i o n c u r v e s f o r b o t h key b a s i n s are drawn
o n f i g u r e 11 a f t e r b e i n g r e d u c e d t o 5 km 2 . The f i n a l network for a l l t h e s t a n d a r d b a s i n s is g i v e n on f i g u r e 12.
3.5. P r a c t i c a l r u l e s f o r water r e s o u r c e s a s s e s s m e n t
. Measuring t h e s u r f a c e of t h e ca tchment .
. E v a l u a t e t h e median y e a r l y p r e c i p i t a t t o n d e p t h w i t h t h e h e l p of f i g . 1 (P,)
. Deduce from P, t h e d i s t r i b u t i o n c u r v e ( f i g u r e 2)(may b e used i n case of
d e l i c a t e i n t e r p o l a t i o n la ter o n ) .
. S t u d y on t h e f i e l d , o r if i m p o s s i b l e , on aer ia l photographs , of t h e morpho-
log ica l factors of r u n o f f .
. I f t h e b a s i n on s t u d y , w i t h a n area c l o s e t o 5 o r 2 5 km', p r e s e n t s s i m i -
l a r c h a r a c t e r i s t i c s a s one o f t h e s t a n d a r d b a s i n , one can i n t e r p o l a t e a
d i s t r i b u t i o n c u r v e c o r r e s p o n d i n g t o t h e median y e a r l y p r e c i p i t a t i o n e v a l u a -
t e d a s above.
. I f its c h a r a c t e r i s t i c s are i n t e r m e d i a t e between t h o s e o f two s t a n d a r d
b a s i n s of t h e same g e o l o g i c a l class, o n e c a n first draw t h e two d i s t r i b u t i o n
c u r v e s c o r r e s p o n d i n g t o both of t h e s e b a s i n s f o r t h e e s t i m a t e d median y e a r -
l y p r e c i p i t a t i o n s . The . f i n a l c u r v e w i l l b e i n t e r m e d i a t e between t h e s e two
c u r v e s
. I f t h e b a s i n d o e s n o t be long a s t u d i e d class, o n e s h a l l endeavour t o i n -
t e r p r e t a t e its p e r m e a b i l i t y p o s s i b i l i t i e s d u r i n g t h e f i e l d s u r v e y and t o
a d o p t t h e r e f e r e n c e class and s t a n d a r d b a s i n whichseem t o be t h e closest
from t h i s p o i n t of view.
. I f t h e s u r f a c e of t h e ca tchment is v e r y d i f f e r e n t from 5 o r 25 km2, t h e
p r e c e d i n g o p e r a t i o n s must b e made fo r b o t h of t h e s e s u r f a c e s , t h e n t h e
f i n a l c u r v e will b e o b t a i n e d by i n t e r p o l a t i o n .
2 If i n s i d e a v e r y p e r v i o u s c a t c h m e n t , e x i s t s a n i m p e r v i o u s area o f n km , t h e c a t c h m e n t must b e t r e a t e d a s a n i m p e r v i o u s c a t c h m e n t o f n km', i n
n e g l e c t i n g t h e r e m a i n i n g .
4. CONCLUSION
T h i s p a p e r shows t h a t i t is p o s s i b l e t o assess t h e s u r f a c e water re-
s o u r c e s i n a r i d z o n e s even when t h e i n f o r m a t i o n is v e r y r e s t r i c t e d i n t h e s p a c e
and i n t h e time. I n t h e case of A f r i c a n S a h e l , s t u d i e d by Dr. R o d i e r , a l l t h e
i n f o r m a t i o n is c o l l e c t e d i n t h e r e g i o n . With t h e k i n d of a n a l y s i s which h a s been
u s e d , it would be p o s s i b l e t o a p p l y t h e t a b l e s and t h e g r a p h s i n a n o t h e r r e g i o n
b u t under t h e c o n d i t i o n t h a t a l l b a s i c h y p o t h e s e s b e r e s p e c t e d :
- o n e must be s u r e t h a t t h e r e i s a real a n a l o g y between t h e p h y s i o g r a p h i c a l
c h a r a c t e r i s t i c s o f t h e unknown c a t c h m e n t s and t h e s e of t h e s t a n d a r d s
b a s i n s u s e d f o r e s t a b l i s h i n g t h e g r a p h s ;
- t h e climate must b e t h e same i n b o t h r e g i o n s , e s p e c i a l l y f o r t h e t y p e
of p r e c i p i t a t i o n s ( t r o p i c a l storms) s h a p e o f which is v e r y i m p o r t a n t f o r
I 1 5
runoff g e n e r a t i o n .
It s h o u l d be s t r o n g l y recommended t h a t a l l t r o p i c a l c o u n t r i e s pay s p e -
c i a l a t t e n t i o n f o r i n i t i a t i n g o r p u r s u i n g i n v e s t i g a t i o n s i n t h a t f i e ld These
s t u d i e s are e x p e n s i v e b u t n e c e s s a r y f o r a good a s s e s s m e n t of s u r f a c e water re-
s o u r c e s i n a r i d zones . Each new i n f o r m a t i o n c o l l e c t e d anywhere will v a l o r i z e t h e
r e s u l t s a l r e a d y a v a i l a b l e .
- 1 6 - L -
RODIER J . A . - " E v a l u a t i o n d e I ' é c o u l e m e n t annuel d a n s l e
S a h e l T r o p i c a l a f r i c a i n " .
In "Travaux e t d o c u m e n t s d e I'ORSTOM" - no 46
ORSTCM, Paris 1975.
[ 2 ] GIRARD G. - " L e s m o d è l e s h y d r o l o g i q u e s p o u r l ' é v a l u a t i o n
d e l a l a m e é c o u l é e en zone sahe'lienne e t
l e u r s contraintes".
' In " C a h i e r s d e It0RSTOM - S é r i e Hydrologie ' '
Vol . XII-no3 -1975 - p p . 189-221.
[ 3 ] GIRARD G. - " A p p l i c a t i o n d u m o d è l e 2 d i s c x d t i s a t i o n
s p a t i a l e a u bassin d e l ' o u e d Ghorfa ( M a u r i t a -
n ie)" .
In "Cahiers d e 1 'ORSTOM - Série H y d r o l o g i e "
Vol. XII-no 3 -1975 - pp . 167-188.
- 17 -
YEARLY RAINFALL IN AFRICAN SAHEL fig- 1
200c
10oc 9 0 C 80C ?O( 60C
500
40C
300
v zoa
toa
40
20
Frequency distr ibut ion of yearly ra in fa l ls in a f r ican Sahel
(Isohyets 300 to 750mm)
Fig- 2
b
Frequency of excmedwa 0 I
I 0.02 0.05 o1 0.2 0.3 0 4 C
2000
1000 900 800 700 600
500
400
300
zoo
1 0 0
40
20 0.6 0.7 0.8 0.9 o 95 o 98 0.99 0,995
Yearly runof f for b a s h a reas greater t h a n 10000 km’ i n a f r i can Sahel
F i g - 3
2ooc Frequency distribution curves
5 0 . \ \
I -- - - - i%.‘-wL y! u-u, .- c 20.
5 3
2 10,
œ
\ U
c - c
--- ------
5 .
-- - - - - _
2 .
I l l Frequency of arccedence
0.01 0.02 0.05 0.1 0.2 0.3 0.4 O. 1
1 1
c
2
c
-F
I
20 o
100
50
!O
I C
œ .-
5 a U
0 .= C
a
. c
L
t
T
Yearly runof f for basin areas between 1000 and 10000km2 Fig- 4 in a f r i can Sahel
4 Basins on granite and granito-gneiss. tency. distribution curves
tt
+- I I I I I I
2 0.05 0.1 0.2 0.3 0.4 O
I 2 0 0
100
50
. I
!e*
2
c I
.-
O U - P
o
!
9
I
b-
B
Ø
c
9
* ,
.. b
c.
Yearly runoff for basin areas between 1000 and 10000 km* i n a f r i can Sahel
A Basins on various soils (sandstones. schists. marly limestones-.)
Frequency of exceedence 1 I I 0.01 , 0.02 0.05 0.1 0.2 c 0.4 0.5 O
- a
fig- 5
A
c
I 3
,
Yearly runoff for basin a reas between 40 and 1000 km* F i g - 6 t in a f r i c a n Sahel I
200
100
50
20
IO
5
1
I '9
n
I
4 Yearly r u n o f f for b a s i n areas between 40 and 1000km' F ig - 7 300
200
100
50
10
O
I
!
8
. 1
c
4 .
500
400
300
200
100
50
20
10
5
Yearly runoff for bas in area i n a f r i c a n Sahel Fig- 8